A weakly coupled model of differential equations for thief tracking

Simone Göttlich; Camill  Harter

doi:10.3934/nhm.2016004

Article Contents

2016, Volume 11, Issue 3: 447-469. Doi: 10.3934/nhm.2016004

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A weakly coupled model of differential equations for thief tracking

Simone Göttlich^1, and
Camill Harter^1,

1.
Department of Mathematics, University of Mannheim, D-68131 Mannheim

Received: April 2015

Revised: November 2015

Published: September 2016

Abstract / Introduction Related Papers Cited by

Abstract

In this work we introduce a novel model for the tracking of a thief moving through a road network. The modeling equations are given by a strongly coupled system of scalar conservation laws for the road traffic and ordinary differential equations for the thief evolution. A crucial point is the characterization at intersections, where the thief has to take a routing decision depending on the available local information. We develop a numerical approach to solve the thief tracking problem by combining a time-dependent shortest path algorithm with the numerical solution of the traffic flow equations. Various computational experiments are presented to describe different behavior patterns.

Keywords:

Mathematics Subject Classification: Primary: 90B20; Secondary: 65M06.

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